I do get the code behind the cost function, its purpose etc. but do I also need to thoroughly understand the plotting that is used to arrive at the optimal w, b values? The code for 3d contour charts etc seem a bit overwhelming to just test a function with different parameter values. I am trying to understand - if the house prices dataset was the exact use case in the real world, would the engineers plot these charts to test the cost or would they just run the function in a loop for different values of w,b and see which one gets the lowest cost?
The 3D contour plots aren’t significantly important. Note that if a data set has more than three features (which is usually the case), you can’t make a plot anyway. There would be too many dimensions for a plot to be implemented.
The sort of plots that are used tend to be simple 2D plots that show (for example) the trend in the cost value with the iterations. That is sufficient to show if the solution is converging (because the cost will continue to decrease).
as @TMosh said plotting the contours is not that important because in real-world examples the dimensions of the data increased and there will be no way to plot that many dimensions.
But, I want to say that the plot of the Cost Value (Error) over iterations is more important as it should decrease over time and it’s universal as It will be just a numeric value (scalar) regardless of the number of dimensions of the data be used.
this is a real example using a 30 dimensions function
so its not important to plot a chart for each of the iteration, but its useful to plot a simple 2d chart that shows how the cost is changing over iterations. thanks.
@ravid
Exactly, as said above plotting a chart for each step as a contour plot is doable in very narrow cases and with maximum dimensions of 3D like contour, or contourf and contour3d in matplotlib.
unlike plotting the error over iterations does not depend on the number of dimensions all you got is just a scalar value that can be plotted using line plot in matplotlib.